Methods and apparatus for multiple input multiple output (MIMO) successive interference cancellation (SIC) with retransmissions

ABSTRACT

Systems and methods are provided for determining a successive interference cancellation (SIC) decoding ordering in a multiple input multiple output transmission (MIMO) system with retransmissions. A plurality of codewords is transmitted in a current transmission time. Some of the codewords may have been previously transmitted in previous transmission attempts according to a retransmission protocol. The plurality of codewords is received and an ordering metric is computed for a received codeword based on channels associated with multiple transmission attempts of the codeword. A decoding ordering of the codewords is determined based on the computed ordering metric. Performance parameters such as Packet Error Rate (PER), channel gain, and/or equalizer-output Signal-to-Interference and Noise Ratio (SINR) may be used to evaluate a channel quality for each one of the transmission attempts of the codeword. The ordering metric may be updated recursively with each transmission attempt.

CROSS-REFERENCE TO RELATED APPLICATIONS

This present disclosure claims benefit under 35 U.S.C. §119(e) of U.S.Provisional Application No. 61/357,875, filed Jun. 23, 2010, which ishereby incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of theinventors hereof, to the extent the work is described in this backgroundsection, as well as aspects of the description that may not otherwisequalify as prior art at the time of filing, are neither expressly norimpliedly admitted as prior art against the present disclosure.

The disclosed technology relates to communication systems, and moreparticularly, to performing successive interference cancellation (SIC)in multiple input multiple output (MIMO) systems with retransmissions.

In a data transmission system, it is desirable for information, oftengrouped into packets, to be accurately received at a destination. Atransmitter at or near the source sends the information provided by thesource via a signal or signal vector. A receiver at or near thedestination processes the signal sent by the transmitter. The medium, ormedia, between the transmitter and receiver, through which theinformation is sent, may corrupt the signal such that the receiver isunable to correctly reconstruct the transmitted information. Therefore,given a transmission medium, sufficient reliability is obtained throughcareful design of the transmitter and/or receiver, and of theirrespective components.

However, the transmitter may be unaware of how the channel will affect atransmitted signal, and may not be able to transmit information in a waythat will be effective for a particular channel. For example, thetransmitter may be a wireless router, where the channel varies dependingon its surroundings. One technique to increase reliability when thetransmitter does not have information about the channel is to use anerror correction scheme. An error correction scheme functions by addingredundancy to the transmitted information. Therefore, when a reasonablysmall number of errors occurs, there is still enough information to makean accurate determination of the transmitted sequence. The redundancyadded to the transmitted information is determined based on an errorcorrection code, such as a Reed-Solomon or Golay code.

One straightforward way to implement an error correction scheme is touse forward error correction (FEC). The transmitter encodes the dataaccording to an error correction code and transmits the encodedinformation. Upon reception of the data, the receiver decodes the datausing the same error correction code, ideally eliminating any errors.Therefore, “decoding” is hereinafter referred to as a method forproducing an estimate of the transmitted sequence in any suitable form(e.g., a binary sequence, a sequence of probabilities, etc).

Another way to implement a code for error correction is to use automaticrepeat request (ARQ). Unlike FEC, ARQ schemes use error-detecting ratherthan error-correcting codes. The ARQ transmitter encodes data based onan error-detecting code, such as a cyclic redundancy check (CRC) code.After decoding the data based on the error-detecting code, if an erroris detected, the receiver sends a request to the transmitter toretransmit that codeword. Thus, ARQ protocols require a forward channelfor communication from transmitter to receiver and a back channel forcommunication from receiver to transmitter. Ultimately, the receiverwill not accept a packet of data until there are no errors detected inthe packet.

Finally, FEC and ARQ may be combined into what is known as hybridautomatic repeat request (HARQ). One type of HARQ, referred to as HARQtype-I, typically uses a code that is capable of both error-correctionand error-detection. For example, a codeword may be constructed by firstprotecting the message with an error-detecting code, such as a CRC code,and then further encoding the CRC-protected message with anerror-correcting code, such as a Reed-Solomon, Golay, convolutional,turbo, or low-density parity check (LDPC) code. When the receiverreceives such a code, it first attempts FEC by decoding the errorcorrection code. If, after error detection, there are still errorspresent, the receiver will request a retransmission of that packet.Otherwise, it accepts the received vector.

HARQ type-II and type-III are different from HARQ type-I, because thedata sent on retransmissions of a packet are not the same as the datathat was sent originally. HARQ type-II and type-III utilize incrementalredundancy (IR HARQ) in successive retransmissions. That is, the firsttransmission uses a code with low redundancy. The code rate of a code isdefined as the proportion of bits in the vector that carry informationand is a metric for determining the throughput of the information.Therefore, the low redundancy code used for the first transmission of apacket has a high code rate, or throughput, but is less powerful atcorrecting errors. If errors are detected in the first packet, thesecond transmission is used to increase the redundancy, and thereforethe error correcting capability, of the code. For example, if the firsttransmission uses a code with a code rate of 0.80, a retransmission mayadd enough extra redundancy to reduce the overall code rate to 0.70. Theredundancy of the code may be increased by transmitting extra paritybits or by retransmitting a subset of the bits from the originaltransmission. If each retransmission can be decoded by itself, thesystem is HARQ type-III. Otherwise, the system is HARQ type-II.

Successive interference cancellation (SIC) is another technique forimproving the performance of a data transmission system. According tothis technique, a received codeword that is associated with strongchannel conditions is decoded before other codewords that are associatedwith weak channel conditions. Effects of the decoded codeword aresubtracted from a received signal vector to eliminate interference dueto the decoded codeword from the other codewords. In this way, the othercodewords may experience less interference and are able to achieve ahigher Signal-to-Noise Ratio (SNR) than without interferencecancellation.

The order in which codewords are decoded may have an important impact onthe SIC performance. Conventional SIC methods decode codewords in anorder that is based on channel parameters (e.g., channel quality)associated with each received codeword at the receiving time only.However, the channel quality may change over multiple transmissionattempts of the same codeword.

SUMMARY OF THE INVENTION

In view of the foregoing, systems and methods are provided forperforming successive interference cancellation (SIC) in a multipleinput multiple output transmission (MIMO) system with retransmissions.

In some embodiments, a plurality of codewords transmitted in a currenttransmission time is received. The received codewords include at leastone retransmitted codeword that was previously transmitted in a previoustransmission time. For the at least one previously transmitted codeword,an ordering metric is computed based on a first channel associated withthe previous transmission time and a second channel associated with thecurrent transmission time. A decoding ordering of the codewords isdetermined based on the computed ordering metric.

In some implementations, an ordering metric is computed for a receivedcodeword based on the channels associated with any subset of allprevious transmission times corresponding to all previous transmissionattempts of the codeword.

In some implementations, the ordering metric is computed based onperformance parameters such as Packet Error Rate (PER), channel gain,and/or equalizer-output Signal-to-Interference and Noise Ratio (SINR)evaluated over multiple transmission attempts of the codeword.

BRIEF DESCRIPTION OF THE FIGURES

The above and other aspects and potential advantages of the presentdisclosure will be apparent upon consideration of the following detaileddescription, taken in conjunction with the accompanying drawings, inwhich like reference characters refer to like parts throughout, and inwhich:

FIG. 1 is a high level block diagram of a data transmission system, inaccordance with some embodiments of the present disclosure;

FIG. 2 is a high level block diagram of a successive interferencecancellation (SIC) system, in accordance with some embodiments of thepresent disclosure;

FIG. 3 is a flow diagram illustrating a process for performing SIC, inaccordance with some embodiments of the present disclosure;

FIG. 4 illustrates a process for determining a SIC ordering based onchannels associated with a transmission time t, in accordance with someembodiments of the present disclosure;

FIG. 5 is a flow diagram illustrating a process for determining ahistory-aware SIC ordering based on channels associated with at leastone previous transmission attempt of a currently received codeword, inaccordance with some embodiments of the present disclosure;

FIG. 6 is a flow diagram illustrating a process for determining ahistory-aware SIC ordering based on predicted PER, in accordance withsome embodiments of the present disclosure;

FIG. 7A is a flow diagram illustrating a process for determining ahistory-aware SIC ordering using incremental SNR, in accordance withsome embodiments of the present disclosure;

FIG. 7B is a flow diagram illustrating a process for recursivelydetermining a history-aware SIC ordering based on a performance metricassociated with at least one previous transmission attempt of acurrently received codeword, in accordance with some embodiments of thepresent disclosure;

FIG. 8A is a flow diagram illustrating a process for determining ahistory-aware SIC ordering using incremental equalizer-output SINR, inaccordance with some embodiments of the present disclosure;

FIG. 8B is a flow diagram illustrating a process for recursivelyupdating ordering metrics using the incremental SINR approach of FIG.8A, in accordance with some embodiments of the present disclosure;

FIG. 9 illustrates one example of the incremental SINR based orderingapproach of FIG. 8B, in accordance with some embodiments of the presentdisclosure;

FIG. 10A shows a simulated performance of processes for determining SICordering in a closed loop MIMO system using minimum mean square error(MMSE) decoding, in accordance with some embodiments of the presentdisclosure;

FIG. 10B shows a simulated performance of processes for determining SICordering in a closed loop MIMO system using maximum likelihood decoding(MLD), in accordance with some embodiments of the present disclosure;

FIG. 11A shows a simulated performance of processes for determining SICordering in an open loop MIMO system using MMSE decoding, in accordancewith some embodiments of the present disclosure; and

FIG. 11B shows a simulated performance of processes for determining SICorderings in an closed loop MIMO system using MLD, in accordance withsome embodiments of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure generally relates to performing successiveinterference cancellation (SIC) in a multiple input multiple outputtransmission (MIMO) system with a retransmission protocol. In oneaspect, codewords may be ordered based on channels associated with allprevious transmission attempts of the codeword.

FIG. 1 shows an illustration of a data transmission system 100 inaccordance with some embodiments. The system of FIG. 1 includestransmitter 110, channel 160, and receiver 180. In some embodiments,data to be transmitted may be divided between a large number oftransmission systems such as system 100, where each system correspondsto one parallel transmission. For example, system 100 may correspond toone subcarrier that carries data in a particular frequency range, or atone. In some embodiments, the illustrated system may represent awireless communication system. In these embodiments, transmitter 110 maybe a wireless router and receiver 180 may be a wireless receiver, suchas a mobile telephone, computer, laptop, hand held device, or other suchdevice. The components shown in transmitter 110 and receiver 180 may beimplemented by a single integrated circuit (IC) or as separatecomponents in a circuit board or implemented on a programmable logicdevice. These components may be implemented on separate devices orcircuits and networked together.

Transmitter 110 may process C information bit sequences to produce Ccodewords using encoder and modulator blocks. For example, encoder andmodulator blocks 102, 104, and 106 may process bit sequences 101, 103,and 105, to output codewords 112, 114, and 116, respectively. Althoughthe present disclosure is described in terms of binary data, the bitsequences 101, 103, and 105 may be replaced with a sequence ofnon-binary digits or another type of information-containing symbolwithout departing from the scope of the present disclosure. In someembodiments, encoder and modulator blocks 102, 104, and 106 may includeencoders 102 a, 104 a, and 106 a respectively, e.g., that employ errorcorrection or error detection codes to encode bit sequences 101, 103,and 105. For example, encoders 102 a, 104 a, and 106 a may encode bitsequences 101, 103, and 105 using CRC code, convolutional code, Turbocode, LDPC code, or any other suitable code. Encoder and modulatorblocks 102, 104, and 106 may additionally include modulators 102 b, 104b, and 106 b respectively, to modulate the encoded bit sequences of bitsequences 101, 103 and 105 based on any appropriate modulation scheme,such quadrature amplitude modulation (QAM), pulse amplitude modulation(PAM), or phase shift keying (PSK). Although encoder and modulatorblocks 102, 104, and 106 are illustrated as separate blocks, theseblocks may be implemented as one or multiple encoder and modulatorunits.

Codeword to stream mapper 120 may process the C codewords output by theencoder and modulator blocks (e.g., encoder and modulator blocks 112,114, and 116) to output S streams. These S streams are represented bycoded values x₁[m] through x_(S)[m], where m is a transmission indexassociated with a transmission instance. A transmission instance may bedefined in time domain or frequency domain or any combination thereof.In some embodiments, m may refer to the index of symbols sent in thetime domain. In some embodiments, m may represent the index ofsubcarriers (i.e., m=1 indexes a stream that is transmitted first, e.g.,by a first subcarrier and m=2 indexes a stream that is transmittedsecond by a second, possibly different, subcarrier). All S streams x₁[m]through x_(S)[m] may be collectively referred to as a S×1 stream vectorx(m) such that:x(m)=[x ₁ [m], . . . ,x _(S) [m]] ^(T).

Streams x₁[m] through x_(S)[m] may be input into MIMO precoder 150. MIMOprecoder 150 may map stream x₁[m] through x_(S)[m] to transmit values{tilde over (x)}₁[m] through {tilde over (x)}_(T)[m], where T is thenumber of transmit antennas (T≧S). These transmit values may be groupedin a T×1 vector {tilde over (x)}(m), which will be referred tohereinafter as transmit vector {tilde over (x)}(m) where:{tilde over (x)}(m)=[{tilde over (x)} ₁ [m], . . . ,{tilde over (x)}_(T) [m]] ^(T).This mapping from stream vector x to transmit vector {tilde over (x)}may be performed using a linear precoding operation. For example, MIMOprecoder 150 may generate transmit vector {tilde over (x)} bymultiplying stream vector {tilde over (x)} by a T×S precoding matrix P,such that:{tilde over (x)}(m)=P(m)x(m).  (EQ. 1a)Precoding matrix P may be chosen to implement certain transmissionschemes. In some embodiments, precoding matrix P may be selected suchthat multiple copies of the same data stream x₁[m] are sent across anumber of transmit antennas to improve the reliability of data transfer.This redundancy results in a higher chance of being able to use one ormore of the received copies to reconstruct the transmitted signals atthe receiver.

Transmit values {tilde over (x)}₁[m] through {tilde over (x)}_(T)[m] maybe transmitted using T transmit antennas through channel 160 andreceived by R receiver antennas at receiver 180. For example, {tildeover (x)}₁[m] may be transmitted through transmit antenna 152. Duringtransmission, {tilde over (x)}₁[m] through {tilde over (x)}_(T)[m] maybe altered by a transmission medium, represented by channel 160, andadditive noise sources z₁[m] through z_(R)[m]. In a wirelesscommunication system channel 160 may be the physical space between thetransmit and receiver antennas, which obstructs and attenuates thetransmitted signals due to at least time varying multipath fades andshadowing effects. Additive noise sources z₁[m] through z_(R)[m] may,for example, be ambient electromagnetic interference. In some scenarios,noise sources z₁[m] through z_(R)[m] may be modeled as additive whiteGaussian noise (AWGN) with zero mean. Also, in many applications,channel 160 may be time invariant, meaning that the properties of thechannel do not substantially change over an appropriate time scale. Inreal time data transmission systems, an appropriate time scale may be inthe millisecond range.

Receiver 180 may receive signals y₁[m] through y_(R)[m] using R receiverantennas such as receiver antenna 182. These received signals will becollectively referred to as the m^(th) received vector y(m), or simplythe received vector y, where:y(m)=[y ₁ [m], . . . ,y _(R) [m]] ^(T).Receiver 180 may include any suitable number of receiver antennas, andtherefore R may be any integer of at least S. Signals y₁[m] throughy_(R)[m] may include information from one or more of signals {tilde over(x)}₁[m] through {tilde over (x)}_(T)[m] that have been attenuatedand/or corrupted by channel 160 and noise sources z₁[m] throughz_(R)[m]. Receiver 180 may process the received signals to produceoutput bit sequence 191. The processing done by receiver 180 may includedemodulation and decoding. Alternatively, output bit sequence 191 may bedirected to a decoder (not shown) external to receiver 180.

Because of the multiple transmit antennas of transmitter 110 and thepossibly multiple receiver antennas of receiver 180, channel 160 maysometimes be referred to as a MIMO channel with T inputs (fromtransmitter 110) and R outputs (to receiver 180), or simply a T×R MIMOchannel. Due to channel properties, the signal received by each of the Rreceiver antennas may be based on signals from multiple transmitantennas. In particular, a signal received by each receiver antenna maybe a linear combination of the signals provided by the transmitantennas. Thus, in matrix form, the m^(th) received vector r(m) can bemodeled by:y(m)={tilde over (H)}(m){tilde over (x)}(m)+z(m),m=1, . . . ,M,  (EQ.1b)where M is the total number of received coded symbol vectors, y is theR×1 received vector representing the signals received by the R receiverantennas of receiver 180, and {tilde over (H)} is a T×R matrixrepresenting the effect of channel 160 on transmit vector {tilde over(x)}, and may sometimes be referred to as a channel response matrix.Vector {tilde over (x)} is a T×1 vector containing the transmit valuestransmitted by the T transmit antennas of transmitter 110, and z is anR×1 signal vector representing additive noise, where z(m)=[z₁[m], . . ., z_(R)[m]]^(T).

Substituting EQ. 1a into EQ. 1b, one can compute an effectivetransmission channel relating the stream vector x to the received vectory as follows:y(m)={tilde over (H)}(m)P(m)x(m)+z(m)=H(m)x(m)+z(m),  (EQ. 2)where {tilde over (H)}(m) represents the actual channel characteristicsused in channel 160 and H(m)={tilde over (H)}(m)P(m)=[h₁[m], . . . ,h_(S)[m]] is a R×S matrix representing the effective transmissionchannel as modified by precoder 150. In some embodiments, the precodingmatrix P can be chosen such that an effective transmission channel H(m)is created that maximizes the diversity gain of the system. For example,precoding matrix P may be chosen to change the apparent characteristicsof the channel so that the effective channel matrix is more orthogonalthan the actual channel matrix. Precoding matrix P may be a Givensrotation matrix, a Vandermonde matrix, a Fourier matrix, a Hadamardmatrix or another type of matrix.

Each codeword, e.g., codeword 112, may be mapped to a set of streamsx_(i) ₁ [m] through x_(i) _(c(i)) [m] (where c(i) denotes the totalnumber of streams corresponding to codeword i, 1≦c(i)≦S). In otherwords, an i^(th) codeword (equivalently codeword i, or codewordassociated with index i) may be associated with a set of stream indicesS_(i)={i₁, i₂, . . . , i_(c(i))}, such that the stream vector x_(i)(m)coming from the i^(th) codeword is expressed as:x _(i)(m)=[x _(i) ₁ [m], . . . ,x _(i) _(c(i)) [m]] ^(T).Similarly, the channels corresponding to the i^(th) codeword(alternatively codeword i) may be expressed using stream indices fromthe stream set S_(i) as follows:H _(i)(m)=[h _(i) ₁ [m], . . . ,h _(i) _(c(i)) [m]].

In some embodiments, transmitter 110 and receiver 180 may employ aretransmission protocol that allows transmitter 110 to transmit the sameinformation to receiver 180 multiple times. For example, transmitter 110and receiver 180 may employ an automatic repeat request (ARQ) or hybridautomatic repeat request (HARQ) scheme. When an ARQ or HARQ scheme isused, receiver 180 may include back channel transmitter 115. Transmitter115 may be operable to send acknowledgement signals back to transmitter110 through backchannel 107. An affirmative acknowledgement signal maybe sent by transmitter 115 in response to a successful transmission,while a negative or no acknowledgement signal may be sent if atransmission is not successful. A successful transmission is one wherethe received signal y is reconstructed and accepted by receiver 180.Receiver 180 may accept reconstructed information when, for example, itdoes not detect any errors (e.g., from a CRC check) in the reconstructedinformation. The reconstruction process may include decoding, diversitycombining, signal processing, another technique or a combinationthereof.

While the present invention is described primarily with respect to ARQand HARQ retransmission protocols, other retransmission protocols mayalso be used. For example, a transmission system may employ a repetitioncoding and transmission protocol, where a fixed number ofretransmissions are sent for every data packet that is transmittedirrespective of the number of transmissions needed by the receiver. Inthis case, because retransmission requests may not be needed toimplement the retransmission protocol, transmitter 115 may not beneeded.

A transmission may be defined as a Transmission Time Interval (TTI) anda transmission time t may be defined as the index of a particular TTI.In an exemplary Long Term Evolution (LTE) implementation, a subframe maycorrespond to a TTI for the Physical Downlink Shared Channel (PDSCH),and transmission time t may correspond to an identifier of the subframe(i.e., t=Subframe_ID). From a plurality of C codewords transmitted at atransmission time t, each codeword of the C codewords may have beentransmitted by transmitter 110 a different number of transmissionattempts k_(i). For example, a transmission time t may correspond to asecond transmission attempt of codeword 1 (k₁=2) and a firsttransmission attempt of codeword 2 (k₂=1). The transmission time tcorresponding to the k_(i) ^(th) transmission attempt of codeword i maybe expressed using function t_(i)( ) as follows:t=t _(i)(k _(i)).In the following description, the transmission time t may sometimes beomitted to simplify the notation.

The system model of EQ. 2 may be extended to account for theretransmission capabilities of MIMO system 100 as follows:

${{y(m)} = {{{{H(m)}{x(m)}} + {z(m)}} = {{\sum\limits_{i = 1}^{C}{{H_{i}^{(k_{i})}(m)}{x_{i}^{(k_{i})}(m)}}} + {z(m)}}}};$m = 1  …  M(t),where M(t) is the total number of received coded symbol vectors attransmission time t (e.g., the t^(th) TTI), y is the R×1 received vectorrepresenting the signals received by the R receiver antennas of receiver180 at a receiving time corresponding to transmission time t, and z isan R×1 signal vector representing additive noise with noise varianceσ^((t)2) associated with transmission time t. Channel H is a T×R matrixrepresenting the effect of channel 160 on transmit vector x. Channel Hmay be expressed using channel components H_(i) ^((k) ^(i) ⁾ (i=1, . . ., C), where each channel component H_(i) ^((k) ^(i) ⁾ represents theportion of channel H corresponding to codeword i under its k_(i) ^(th)transmission attempt at time t. Channel may also be expressed usingchannel components h_(s)(m;t) (s=1, . . . , S), where each channelcomponent h_(s)(m;t) represents the portion of channel H correspondingto stream s transmitted at transmission time t. Both representations ofchannel H are shown in the following:H(m;t)=H(m)=[H ₁ ^((k) ¹ (m) . . . H _(C) ^((k) ¹ ⁾(m)]=[h ₁(m;t) . . .h _(S)(m;t)].Vector x is a T×1 vector containing the transmit values transmitted bythe T transmit antennas of transmitter 110 at transmission time t asfollows:x(m;t)=x(m)=[(x ₁ ^((k) ¹ ⁾(m))^(T) . . . (x _(C) ^((k) ^(C)⁾(m))^(T)]^(T).At the transmission time t, each transmit value x_(i) ^((k) ^(i) ⁾ maycorrespond to a transmission attempt k_(i). In the following descriptionand for purposes of illustration, x(m;t) may be simply denoted as x(m)or x.

The same transmit values may be transmitted during multiple transmissionattempts of a same codeword. Alternatively, different transmit valuesmay be transmitted. For example, a transmit value x_(i) ^((k))(m) of acodeword i transmitted during transmission attempt k may be differentfrom a transmit value x_(i) ^((j))(m) of the same codeword i transmittedduring another transmission attempt j. This is the case, for example,when incremental redundancy (IR HARQ) is used in successivetransmissions.

One technique for improving the performance of a MIMO system, e.g., ofsystem 100 of FIG. 1, is to use successive interference cancellation(SIC). According to this technique, a codeword associated with strongchannel conditions may be decoded first before other codewordsassociated with weaker channel conditions. Effects of this decodedcodeword may be subtracted from a received signal vector, e.g., receivedvector y of FIG. 1, to eliminate interference of the decoded codeword onthe other codewords.

SIC can be implemented in a number of ways. For example, SIC can beimplemented such that all codewords are decoded in parallel, such thatone codeword is serially decoded at each stage, or such that anyarbitrary number of codewords is decoded simultaneously at each stage.Techniques for implementing SIC are described, for example, inco-pending, commonly-assigned U.S. patent application Ser. No.13/047,056, entitled “MULTIPLE-INPUT MULTIPLE-OUTPUT RECEIVERS USINGSUCCESSIVE INTERFERENCE CANCELLATION BASED ON CYCLE REDUNDANCY CHECK”,filed Apr. 2, 2010, which is hereby incorporated by reference herein inits entirety. Hereafter, and for the purposes of illustration, thisdisclosure will primarily discuss the serial SIC implementation. Thesystems and methods of this disclosure, however, may apply to otherimplementations of SIC. For example, any SIC implementation (e.g.,serial or parallel) may use the SIC ordering generated using thetechniques described herein.

FIG. 2 illustrates a block diagram of system 200 for performing SICaccording to some embodiments. System 200 may include C decoding stages1, 2, . . . , C for respectively decoding codewords L₁, L₂, . . . ,L_(C). For ease of illustration, only 4 of the stages are shown, and thestages are chosen to correspond, respectively, to codewords 1, 2, . . ., C in that order (i.e., L₁=1, L₂=2, . . . , L_(C)=C). However, anydesired ordering of codewords may be used, as will be explained infurther detail below.

Each stage (except the last stage) may include a receiver block for acodeword i and an interference canceller associated with that codewordi. For example, receiver block 202 and interference canceller 204 maycorrespond to the first stage associated with codeword 1, receiver block206 and interference canceller 208 may correspond to the second stageassociated with codeword 2, and receiver block 256 and interferencecanceller 258 may correspond to the C−1^(th) stage associated withcodeword C−1. The last stage may include a receiver block associatedwith codeword C and no interference canceller block, for example,receiver block 260. Although the receiver and interference cancellerblocks of FIG. 2 are illustrated as separate blocks, these blocks may beimplemented as one or multiple components by a single or multipleintegrated circuit boards or devices.

At the first stage, receiver 202 may decode codeword 1 based on areceived signal vector y, e.g., received signal vector y from FIG. 1, togenerate decoded codeword 1. Interference canceller 204 may receivereceived signal vector y as well as the decoded codeword 1, as output byreceiver 202. Interference canceller 204 may generate aninterference-free received signal vector ŷ₂, where the interference dueto codeword 1 is cancelled.

At the second stage, receiver 206 may decode codeword 2 based on theinterference-free received signal vector ŷ₂ to generate decoded codeword2. Interference canceller 208 may also receive ŷ₂ from interferencecanceller 204 as well as the decoded codeword 2 output by receiver 206.Interference canceller 208 may generate an interference-free receivedsignal vector ŷ₃, where the interferences due to codewords 1 and 2 arecancelled by removing the effect of codeword 2 from theinterference-free received signal vector ŷ₂.

Similarly to the second stage, a receiver block at an SIC stage i (i=3,. . . , C−1) may decode a codeword i based on an interference-freereceived signal vector ŷ_(i). An interference canceller may output aninterference-free received signal vector ŷ_(i+1), where theinterferences due to codewords 1 through i are cancelled.

At the last stage, receiver block 260 may decode codeword C based oninterference-free received signal vector ŷ_(C) as output by interferencecanceller 258 of stage C−1.

One example of a SIC process that can be implemented in receiver andinterference canceller blocks of FIG. 2 is illustrated in FIG. 3. FIG. 3is a flow diagram illustrating process 300 for performing SIC at atransmission time t using an exemplary codeword ordering (L₁, L₂, . . ., L_(C)). Process 300 includes 302, 304, 306, 308, 310, 312, 314, and316. Process 300 includes 302, 304, 306, 308, 310, 312, 314, and 316. Insome embodiments, 310 may be implemented in receiver blocks of FIGS. 2and 312, 314, and 316 may be implemented in interference cancellerblocks of FIG. 2.

At 302, an ordering for decoding codewords in respective stages of theSIC process at a transmission time t is determined. This ordering may berepresented mathematically as follows:{1,2, . . . ,C}→Π ^((t))=(L ₁ ,L ₂ , . . . ,L _(C)).  (EQ. 3)In other words, the C codewords (e.g., codewords 101 through 105 ofFIG. 1) are mapped to an ordered C-tuple or ordering Π. The tuple Πdefines the order in which the codewords may be decoded at each SICstage i (i=1, . . . , C). In the example illustrated in FIG. 2,codewords 1 through C were decoded in that order (i.e., L_(i)=i).However, any suitable ordering Π may be used. Techniques for determiningSIC decoding ordering are described, for example, in co-pending,commonly-assigned U.S. patent application Ser. No. 13/164,111, entitled“METHODS AND APPARATUS FOR MULTIPLE INPUT MULTIPLE OUTPUT (MIMO)SUCCESSIVE INTERFERENCE CANCELLATION (SIC)”, filed Jun. 20, 2011, whichis hereby incorporated by reference herein in its entirety.

At 304, parameters for process 300 may be initialized. For example, theinterference-free received signal vector ŷ₁ used by the first stage(e.g., received by the interference cancellation block 204 of FIG. 2)may be initialized to the received signal vector y. In addition, theeffective channel matrix Ĥ₁ for the first stage (e.g., used by thereceiver 202 and/or interference canceller 204 of FIG. 2) may beinitialized to the effective channel matrix H (e.g., effective channel130 of FIG. 1).

At 306, it is determined whether all C codewords have been decoded. Ifall codewords have been decoded (i.e., i>C), process 300 may beterminated. Otherwise, if there is any codeword still undecoded (i.e.,1≦i≦C), the codeword may be decoded using 308, 310, 312, 314, and 316.Each iteration for decoding one codeword may correspond to one SICstage.

At 308, a codeword to be decoded at SIC stage i is selected. Forexample, the codeword i to be decoded at SIC stage i may be determinedto be L_(i), as defined by the ordering generated at 302.

At 310, the codeword selected at 308, e.g., the L_(i) ^(th) codeword,may be demodulated and/or decoded based on the interference-free signalreceived at the i^(th) stage, and the SIC-adjusted effective channelmatrix at the i^(th) stage, Ĥ_(i).

This effective channel matrix corresponds to the composite channels forthe codewords that have not been decoded at the i−1^(th) stage, i.e.,Ĥ_(i)=[H_(L) _(i) , . . . , H_(L) _(C) ]. The specific demodulation anddecoding methods used at 310 may depend on the receiver implementation.

At 312, the transmitted signal vector is re-encoded and modulated togenerate reconstructed transmitted signal vector {circumflex over(x)}_(L) _(i) that takes into account the interference cancellation dueto the L_(i) ^(th) codeword. This reconstructed vector may also be knownas a feedback signal.

At 314, the interference-free received signal vector ŷ_(i+i) for stagei+1 is generated by cancelling the interference from theinterference-free received signal vector ŷ_(i) for stage i. This may bedone by subtracting the effect of the reconstructed transmitted signalvector {circumflex over (x)}_(L) _(i) (i.e., as modified by the channels

Ĥ_(L_(i))^((k_(L_(i))))(m)corresponding to codeword L_(i)) from the interference-free receivedsignal vector ŷ_(i):

ŷ_(i + 1)(m) = ŷ_(i)(m) − H_(L_(i))^((k_(L_(i))))(m)x̂_(L_(i))(m).

At 316, the effective channel for the (i+1)^(th) stage, Ĥ_(i+1) may begenerated. For example, Ĥ_(i+1) may be generated by deleting the columnscorresponding to the channels for the L_(i) ^(th) codeword as follows:

Ĥ_(i + 1)(m) = Ĥ_(i)(m) ∖ H_(L_(i))^((k_(L_(i))))(m),where A\B denotes the deletion of columns of the matrix B from thematrix A.

Next, 306 may be checked again. The next codeword, L_(i+1), may bedecoded next (i.e., i is incremented to i+1), unless all codewords havebeen decoded, in which case process 300 may be terminated.

Although process 300 describes SIC using iterative stages, this is meantto be illustrative and is not meant to be limiting or exhaustive. Themethods and processes described herein generally apply to otherrepresentations of SIC, including QR representation.

FIG. 4 illustrates process 400 for determining a SIC ordering based onchannels associated with a transmission time t in accordance with someembodiments. Process 400 includes 402, 404, and 406 and may beimplemented in processing circuitry of receiver 180 of FIG. 1 orreceiver/interference cancellation blocks of FIG. 2.

At 402, a plurality of codewords is received. These codewords may betransmitted at a transmission time t. In some embodiments, atransmission time t may be defined as an index of a particulartransmission time interval (TTI). For example, a subframe may correspondto a TTI for the Physical Downlink Shared Channel (PDSCH) of an LTEimplementation, and transmission time t may correspond to an identifierof that subframe (i.e., t=Subframe_ID).

At 404, an ordering metric γ_(i)(t) is computed for each codeword i ofthe received codewords that have been transmitted at transmission timet. This ordering metric may be determined based on a channel qualityassociated with codeword i at the transmission time t. In someembodiments, e.g., when MIMO system 100 does not implement aretransmission protocol, or when receiver 180 does not consider previoustransmissions of currently received codewords, the ordering metric maynot consider any previous transmission times associated with previoustransmission attempts of codeword i. Such an approach will be referredto herein as a history-free SIC ordering approach. For example, orderingmetric γ₁(t) may be computed for channels associated with transmissiontime t as follows:γ_(i)(t)=f(H(m;t),σ^((t)2);1≦m≦M(t));1≦i≦C,  (EQ. 4),where function f maps effective channel H over M(t) coded symbol vectorsof codeword i to a channel quality using, e.g., a specific performancemetric. Any suitable performance metric may be used, such as the MinimumMean Square Error (MMSE) criterion or the Zero Forcing (ZF) criterion.

In some embodiments, the ordering metric for codeword i transmitted attransmission time t may be computed based on the average channel gainfor codeword i as follows:

$\begin{matrix}{{{\gamma_{i}(t)} = {\frac{1}{{M(t)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{(t)}}{{h_{s}\left( {m;t} \right)}}^{2}}}}}{{1 \leq i \leq C},}} & \left( {{EQ}.\mspace{14mu} 5} \right)\end{matrix}$where |h_(s)(m;t)| is the norm of the channel corresponding to a streams in the stream set S_(i) of codeword i at transmission time t. Channelnorms ∥h_(s)∥ are averaged over all streams corresponding to codeword i(i.e., all streams s in stream set S_(i)) and over all received codedsymbol vectors of codeword i (i.e., symbols m=1, . . . , M(t)) tocompute the ordering metric γ_(i)(t).

At 406, an ordering Π^((t)) from the computed ordering metrics γ_(i)(t)is determined. This ordering may be represented as:Π=(L ₁ ,L ₂ , . . . ,L _(C)),where L_(i) (i=1, . . . , C) is the i^(th) codeword to decode in thatparticular ordering Π^((t)). In some embodiments, the ordering definedin Π^((t)) may be determined from sorting the codewords based on theirordering metrics γ_(i)(t) from highest to lowest. This may berepresented as:Π^((t))={(L ₁ ,L ₂ , . . . ,L _(C))|γ_(L) ₁ ≧ . . . ≧γ_(L) _(C) }.  (EQ.6)

As explained above, a history-free SIC ordering may be determined basedon channel qualities associated with a current transmission time twithout accounting for previous transmission attempts of retransmittedcodewords. However, limiting the SIC ordering to the channel qualitiesat the receiving time only (e.g., corresponding to a currenttransmission time t) may cause degradation of performance in a systemwith retransmissions. This is because channel qualities associated withprevious transmission attempts may impact the order of codewords todecode during a current transmission attempt. For example, during thecurrent transmission time t, a retransmitted codeword n associated withweak channel conditions may have a better decoding opportunity thananother codeword m associated with stronger channel qualities and thathas not been previously transmitted. Accordingly, and according toaspects of this disclosure, a SIC ordering may be determined that takesinto account previous transmission attempts of codewords transmittedduring the current transmission time t. Such a SIC ordering will bereferred to herein as history-aware SIC ordering. By recognizing that acodeword's opportunity of successful decoding may depend not only onchannels at a current transmission time but also on channels at previoustransmission times corresponding to previous transmission attempts, aSIC ordering may achieve a better performance. Various kinds ofperformance criteria can be used to assess channel qualities associatedwith each codeword. Examples of such channel qualities include, but arenot limited, to packet error rate (PER), Signal-to-Noise ratio (SNR),Signal-to-Interference and Noise Ratio (SINR), and/or achievabledata-rate. Embodiments of history-aware SIC ordering processes will bedescribed in further detail below.

FIG. 5 is a flow diagram illustrating process 500 for determining ahistory-aware SIC ordering based on channels associated with at leastone previous transmission attempt of a currently received codeword, inaccordance with embodiments of the present disclosure. Process 500includes 502, 504, and 506, and may be implemented in processingcircuitry of receiver 180 of FIG. 1 or receiver/interferencecancellation blocks of FIG. 2.

At 502, a plurality of codewords may be received that have beentransmitted at transmission time t. This may be done similarly to 402 ofFIG. 4 above.

At 504, an ordering metric γ_(i)(t) is computed for each codeword i ofthe plurality of codewords received at 502. The ordering metric γ_(i)(t)may be based on channels corresponding to multiple transmission timesassociated, respectively, with multiple transmission attempts ofcodeword i. For example, the ordering metric γ_(i)(t) may be based onchannels associated with all transmission times τ=t_(i)(1), . . . ,t_(i)(k_(i)), where t_(i)(1) represents the transmission time of thefirst transmission attempt of codeword i and t_(i)(k_(i)) represents thetransmission time of the last transmission attempt of codeword i at acurrent (or last) transmission time t (i.e., t=t_(i)(k_(i))). This maybe represented as follows:γ_(i)(t)=f(H(m;τ),σ^((τ)2);1≦m≦M(τ),τ=t _(i)(1) . . . t _(i)(k_(i)));1≦i≦C,  (EQ. 7),where the channel H(m;τ) represents the channel associated with thecoded symbol vectors m for codeword i (m=1, . . . , M(τ)) transmitted ata transmission time τ and σ^((τ)2) is the noise variance associated withthe transmission channel at transmission time τ. Mapping function f mayuse any suitable performance criterion, such as predicted PER, SNR,and/or SINR.

Although EQ. 7 considers all transmission times T=t_(i)(1), . . . ,t_(i)(k_(i)), starting from the first transmission attempt of codeword ithrough the last transmission attempt of codeword i, any appropriatesubset of τ may be used in the computation of the ordering metricγ_(i)(t). For example, only a last number of transmission attempts maybe used.

At 506, a decoding ordering Π^((t)) is determined based on the orderingmetrics computed at 504. In some embodiments, the ordering Π^((t)) to beused for codewords associated with transmission time t may be determinedfrom sorting the codewords based on their ordering metrics γ_(i)(t). Forexample, the first codeword to be decoded using SIC, L₁, may have thehighest ordering metric γ_(L) ₁ and the second codeword to be decodedusing SIC, L₂, may have the second highest ordering metric γ_(L) ₂ , andso on, as follows:Π^((t))={(L ₁ ,L ₂ , . . . ,L _(C))|γ_(L) ₁ ≧ . . . ≧γ_(L) _(C) }.

In some embodiments, an ordering metric for a codeword may be computedusing a probability that an error occurred in the received codeword.This probability may be evaluated using a packet error rate (PER), whichmay be calculated as the number of erroneously received data packetsdivided by the total number of received packets. In some embodiments,instead of decoding all codewords in a SIC ordering and computing thePER for each decoded codeword in that ordering based on channelqualities of all transmission attempts of the codeword, PER may bepredicted from the channel information. An example of this is shown inFIG. 6 below.

FIG. 6 is a flow diagram illustrating process 600 for determining ahistory-aware SIC ordering based on predicted PER associated with atleast one previous transmission attempt of a currently receivedcodeword, in accordance with embodiments of the present disclosure.Process 600 includes 602, 604, and 606, and may be implemented inprocessing circuitry of receiver 180 of FIG. 1 or receiver/interferencecancellation blocks of FIG. 2.

At 602, and for each received codeword i that is transmitted attransmission time t, effective channels associated with multipletransmission attempts of codeword i (up to a current transmissionattempt kJ may be mapped to effective SNR values corresponding tocodeword i. For example, channels associated with codeword i over aplurality of transmission times corresponding to the first through thek_(i) ^(th) transmission attempt of codeword i may be mapped to an SNRvalue for each unique coded symbol associated with codeword i. This maybe represented as follows:{H(m;τ),σ^((τ)2);1≦m≦M(τ),τ=t _(i)(1) . . . t _(i)(k _(i))}→{SNR _(eff)^((i))(n;t); 1≦n≦N _(i)(k _(i))},  (EQ. 8),where H(m;τ) represents the effective channel associated with the M(τ)coded symbols for codeword i at transmission time τ (τ=t_(i)(1), . . . ,t_(i)(k_(i))) and σ^((τ)2) is the noise variance associated with thetransmission channel at transmission time τ. N_(i)(k_(i)) represents thetotal number of unique transmitted coded symbols of codeword i up to andincluding the k_(i) ^(th) transmission attempt. Specifically, duringmultiple transmission attempts of codeword i, the same transmitted codedsymbol of codeword i may be repeated. N_(i)(k_(i)) is the number ofunique transmitted coded symbols among all transmitted coded symbols ofcodeword i up to and including the k_(i) ^(th) transmission attempt. Forexample, if there are two transmission attempts (i.e., k_(i)=2) ofcodeword i, such that coded symbols {s₁, s₂} are transmitted in thefirst transmission and coded symbols {s₁, s₃} are transmitted in thesecond transmission, then N_(i)(k_(i)=2) is 3 because there are threeunique transmitted coded symbols s₁, s₂, and s₃. The valueSNR^((i))(n;t) is the effective codeword SNR value per unique codedsymbol n accumulated up to and including the k_(i) ^(th) transmissionattempt associated with codeword i. In this determination ofSNR^((i))(n;t), the effective SNR values of repeated coded symbolvectors may be combined over all transmission attempts of codeword i togenerate the SNR values associated with the unique coded symbols.Continuing the example above, the SNR for both occurrences of s₁ may becombined to compute one SNR value for s₁ (e.g.,SNR^((i))(s₁)=SNR(s₁;1)+SNR(s₁;2)).

The particular mapping from the channels to the effective SNR values(e.g., of EQ. 8) may depend on the type of equalizer (e.g., MMSE), theerror compensation method, the HARQ combining method, and/or the mappingmethod. Examples of the mapping method include, but are not limited to,finite alphabet capacity (FAC), mean mutual information per bit (MMIB),and exponential effective SNR mapping (EESM).

At 604, and for each codeword i (1≦i≦C), the effective SNR valuescomputed at 602 are combined to generate a predicted PER value P_(i)^((k) ^(i) ⁾ codeword i at transmission time t. The effective SNR valuesSNR^((i))(n;t) per unique symbol n may be combined over all uniquetransmitted coded symbols of codeword i up to the transmission time t.For example, the effective SNR values SNR^((i))(n;t) may be averagedover all unique coded symbols n (i.e., n=1, . . . , N_(i)(k_(i))), andthe computed average effective codeword SNR may be mapped to thepredicted PER value P₁ ^((k) ^(i) ⁾ as follows:

$\begin{matrix}{{P_{i}^{(k_{i})} = {F_{{coding}\text{-}{rate}}\left( {\frac{1}{N_{i}\left( k_{i} \right)}{\sum\limits_{n = 1}^{N_{i}{(k_{i})}}{{SNR}_{eff}^{(i)}\left( {n;t} \right)}}} \right)}},} & \left( {{EQ}.\mspace{14mu} 9} \right)\end{matrix}$where F_(Coding-Rate) corresponds to a PER mapping function. In someembodiments, this function may be implemented using look-up tables thatmap various ranges of average effective codeword SNR values to PERvalues at different coding rates. These tables may be based onpre-collected statistics at different coding rates.

At 606, an ordering Π^((t)) may be determined based on the PER value foreach codeword. For example, the codewords may be ordered in increasingorder of their corresponding PER value as follows:

Π^((t)) = {(L₁, …  L_(C))|P_(L₁)^((k_(L₁))) ≤ P_(L₂)^((k_(L₂))) ≤ … ≤ P_(L_(C))^((k_(L_(C))))}.This is similar to the ordering defined in EQ. 6, where the orderingmetric γ_(i)(t) is set to the probability of successful transmission ofcodeword i at transmission attempt k_(i) (i.e., γ_(i)=1−P_(i) ^((k) ^(i)⁾).

In some embodiments, PER may be difficult to estimate. This may be dueto the high complexity of computing the SNR values corresponding to thevarious retransmissions (e.g., EQ. 8), and/or to the difficulty ofobtaining precise PER statistics for each code rate (e.g., functionF_(Coding-Rate) of EQ. 9). A number of history-aware SIC orderingapproaches may be used that approximate the PER for each codeword. Anincremental SNR approach is illustrated in FIGS. 7A and 7B, where PER isrepresented using SNR (or channel gain). An incremental SINR approach isillustrated in FIGS. 8A and 8B, where PER is represented usingequalizer-output SINR. These performance metrics (i.e., SNR and SINR)are merely illustrative, and any performance metric may be used, asappropriate, to measure the performance of a codeword.

FIG. 7A is a flow diagram illustrating process 700 for determining ahistory-aware SIC ordering using incremental SNR, in accordance withembodiments of the present disclosure. Process 700 includes 702 and 704,and may be implemented in processing circuitry of receiver 180 of FIG. 1or receiver/interference cancellation blocks of FIG. 2.

At 702, for each codeword i that is transmitted at transmission time t,effective SNR values (or channel gains) associated with multipletransmission attempts of codeword i may be combined to generate anordering metric. Various types of combinations may be used to combinethese channel gains. For example, channel gains as described in EQ. 5above may be added over the transmission times corresponding to thefirst through k_(i) ^(th) transmission attempt of codeword i (i.e., fortransmission times τ=t_(i)(1), . . . , t_(i)(k_(i))), as follows:

$\begin{matrix}{{\gamma_{i}^{(k_{i})} = {\sum\limits_{j = 1}^{k_{i}}\left( {\frac{1}{{M\left( {t_{i}(j)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(j)}})}}{\frac{1}{\sigma^{{({t_{i}{(j)}})}2}}{{h_{s}\left( {m;{t_{i}(j)}} \right)}}^{2}}}}} \right)}},} & \left( {{EQ}.\mspace{14mu} 10} \right)\end{matrix}$where the operand of the outer summation represents the channel gainassociated with transmission times t_(i)(j) of the j^(th) transmissionattempt. As shown in EQ. 10, these channel gains may be summed over alltransmission attempts (j=1, . . . , k_(i)) of codeword i to compute theordering metric γ_(i) ^((k) ^(i) ⁾ (equivalently, γ_(i)(t) wheret=t_(i)(k_(i))).

Any combination function may be used at 702 to combine channel gainsassociated with the various transmission attempts of a receivedcodeword. For example, instead of the linear sum shown in EQ. 10, ageometric sum may be used as follows:

$\begin{matrix}{\gamma_{i}^{(k_{i})} = {\sum\limits_{j = 1}^{k_{i}}{{\log_{2}\left( {1 + {\frac{1}{{M\left( {t_{i}(j)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(j)}})}}{\frac{1}{\sigma^{{({t_{i}{(j)}})}2}}{{h_{s}\left( {m;{t_{i}(j)}} \right)}}^{2}}}}}} \right)}.}}} & \left( {{EQ}.\mspace{14mu} 11} \right)\end{matrix}$These combination functions are merely illustrative, and are not meantto be limiting or exhaustive in any way. Any combination function may beused to combine channel gains, as appropriate.

At 704, a decoding order Π^((t)) may be determined based on the orderingmetrics for each codeword. For example, the decoding order may bedetermined by sorting the codewords based on their ordering metrics(i.e., the respective incremental channel gain) from highest to lowest,i.e.,

Π^((t)) = {L₁, …  L_(C)|γ_(L₁)^((k_(L₁))) ≥ γ_(L₂)^((k_(L₂))) ≥ … ≥ γ_(L_(C))^((k_(L_(C))))}.

In some embodiments, the combination of performance metrics, e.g., thesum of SNR values in EQS. 10 or 11, may be computed iteratively at eachtransmission attempt. In some embodiments, this combination may becomputed recursively, as shown in FIG. 7B below.

FIG. 7B is a flow diagram illustrating process 750 for recursivelydetermining a history-aware SIC ordering based on a performance metricassociated with at least one previous transmission attempt of acurrently received codeword, in accordance with embodiments of thepresent disclosure. Processes 600 of FIG. 6 or 700 of FIG. 7A may beimplemented in this way. Process 750 includes 752, 754, and 756, and maybe implemented in processing circuitry of receiver 180 of FIG. 1 orreceiver/interference cancellation blocks of FIG. 2.

At 752, a first recursive metric γ_(i) ⁽⁰⁾ may be initialized for eachcodeword i prior to a first transmission attempt of codeword i. Forexample, γ_(i) ⁽⁰⁾ may be set to 0.

At 754, at each k_(i) ^(th) transmission attempt of codeword i, a k_(i)^(th) recursive metric γ_(i) ^((k) ^(i) ⁾ is computed based on therecursive metric γ_(i) ^((k) ^(i) ⁻¹⁾ of the previous (k_(i)−1)^(th)transmission attempt. In some embodiments, the recursive metric γ_(i)^((k) ^(i) ⁾ may be computed by combining a channel quality associatedwith the k_(i) ^(th) transmission attempt with the recursive metricy_(i) ^((k) ^(i) ⁻¹⁾, as follows:γ_(i) ^((k) ^(i) ⁾=γ_(i) ^((k) ^(i) ⁻¹⁾ +f(H(m,t _(i)(k_(i)));1≦m≦M(t)),where f is a mapping function that computes a performance metric, e.g.,SNR, based on the channel associated with the k_(i) ^(th) transmissionattempt. This mapping function may be similar to the mapping functiondescribed in EQ. 7 above.

In some embodiments, the channel quality (e.g., f(H(m,t_(i)(k_(i)));1≦m≦M(t)) may correspond to the channel gain as explained in EQ. 5above. In this case, the recursive equations of 752 and 754 may berepresented as follows:

$\begin{matrix}{\mspace{79mu}{{\gamma_{i}^{(0)} = 0}{\gamma_{i}^{(k_{i})} = {\gamma_{i}^{({k_{i} - 1})} + \mspace{124mu}{\frac{1}{{M\left( {t_{i}\left( k_{i} \right)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(k_{i})}})}}{\frac{1}{\sigma^{{({t_{i}{(k_{i})}})}2}}{{{h_{s}\left( {m;{t_{i}\left( k_{i} \right)}} \right)}}^{2}.}}}}}}}}} & \left( {{EQ}.\mspace{14mu} 12} \right)\end{matrix}$This corresponds to the incremental SNR approach, e.g., process 700 ofFIG. 7A above and is a recursive way of computing the ordering metricγ_(i) ^((k) ^(i) ⁾ of EQ. 10.

At 756, it is determined whether codeword i was successfully transmittedduring transmission time t. If codeword i was successfully transmitted,then the corresponding recursive metric is reset to zero (i.e., 752 isperformed). Otherwise, the recursive metric may continue to be updatedat 754.

The recursive implementation described in FIG. 7B above may apply tovarious combination functions and various types of channel qualitiesand/or performance metrics. While the recursive function in EQ. 12implements the linear sum function corresponding to EQ. 10 above, othercombinations, such as the geometric sum of EQ. 11 may also beimplemented in a similar recursive fashion. These recursiveimplementations may reduce complexity and save time and/or memory, asthese implementations may require only saving a last updated value ofthe recursive metric without having to save and/or re-process channelquality information for previous transmission attempts.

In some embodiments, the PER and/or channel quality may be representedusing an equalizer-output SINR. This SINR may correspond to any type ofequalizer, such as MMSE or ZF. This will be illustrated in FIGS. 8A, 8B,and 9 below.

FIG. 8A is a flow diagram illustrating process 800 for determining ahistory-aware SIC ordering using incremental equalizer-output SINR, inaccordance with embodiments of the present disclosure. Process 800includes 802 and 804, and may be implemented in processing circuitry ofreceiver 180 of FIG. 1 or receiver/interference cancellation blocks ofFIG. 2.

At 802, for each received codeword i that was transmitted attransmission time t, an ordering metric may be computed based on anequalizer-output SINR value associated with each one of multipletransmission attempts of codeword i up to the current transmission timet. For example, a stream SINR_(s)(m) value may be computed for a streams and a coded symbol m corresponding to codeword i for each transmissionattempt.

In some embodiments, the SINR_(s)(m) may be calculated as the quotientbetween the average received modulated subcarrier power and the averagereceived co-channel interference power, i.e. cross-talk, from othertransmitters than the useful signal. In some implementations, the SINRvalues may be computed using signal power and noise power estimationselection circuitry and SINR estimate computation circuitry. Thesecomponents may be implemented in the processing circuitry of receiver180 of FIG. 1 or of receiver/interference cancellation blocks of FIG. 2by a single integrated circuit (IC) or as separate components in acircuit board or implemented on a programmable logic device. In theseimplementations, the SINR_(s)(m) may be by estimated by computing anestimated average of the desired signal power (signal power) and anestimated variance of the noise plus interference power (noise power).The SINR corresponds to the ratio of the signal power to the noisepower.

The SINR_(s)(m) values may be combined to compute a codeword SINR valuecorresponding to a transmission attempt j of codeword i. For example,the SINR_(s)(m) values may be averaged over all streams s in the streamset S_(i) of codeword i and over all coded symbol vectors m (m=1, . . ., M(t_(i)(j)) corresponding to codeword i at transmission time t_(i)(j)to compute the codeword SINR value as follows:

${SINR}_{i}^{(j)} = {\frac{1}{{M\left( {t_{i}(j)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(j)}})}}{{{SINR}_{s}^{(j)}(m)}.}}}}$

The ordering metric γ_(i) ^((k) ^(i) ⁾ may be computed by combining,using a specific combination function, the codeword SINR valuescorresponding to codeword i over multiple transmission attempts ofcodeword i (up to the current transmission attempt k_(i)). In oneembodiment, a linear sum may be used to combine these SINR values asfollows:

$\begin{matrix}{{\gamma_{i}^{(k_{i})} = {\sum\limits_{j = 1}^{k_{i}}\left( {\frac{1}{{M\left( {t_{i}(j)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(j)}})}}{{SINR}_{s}^{(j)}(m)}}}} \right)}},} & \left( {{EQ}.\mspace{14mu} 13} \right)\end{matrix}$where SINR_(s) ^((j))m) represents the stream SINR value for the s^(th)stream at the j^(th) transmission attempt of codeword i and the operandof the outer summation represents the codeword SINR value SINR_(i)^((j)) associated with the j^(th) transmission attempt. Any othercombination function may be used to combine the codeword SINR values,for example, a geometric sum.

At 804, a decoding order is determined based on the ordering metricscomputed at 802. In some embodiments, this ordering may be derived bysorting the ordering metrics (i.e., the sums of SINR values) fromhighest to lowest, i.e.,

Π^((t)) = {L₁, …  L_(C)|γ_(L₁)^((k_(L₁))) ≥ γ_(L₂)^((k_(L₂))) ≥ … ≥ γ_(L_(C))^((k_(L_(C))))}.

In some embodiments, the SINR may be updated recursively to reducecomplexity. FIG. 8B is a flow diagram illustrating process 850 forrecursively updating ordering metrics using the incremental SINRapproach of FIG. 8A, in accordance with embodiments of the presentdisclosure. Process 850 includes 802, 804, 806, and 808, and may beimplemented in processing circuitry of receiver 180 of FIG. 1 orreceiver/interference cancellation blocks of FIG. 2.

At 852, an ordering metric γ_(i,before) ^((k) ^(i) ⁾ may be computed foreach codeword i that does not take into account the effect ofinterference cancellation on the decoding of codeword i at its currenttransmission attempt k_(i). This metric will be referred to herein as apre-SIC ordering metric. In some embodiments, the pre-SIC recursivemetric γ_(i,before) ^((k) ^(i) ⁾ may be computed by updating the valueof a recursive metric γ_(i) ^((k) ^(i) ⁻¹⁾ associated with a(k_(i)−1)^(th) transmission attempt. In some embodiments, this recursivemetric γ_(i) ^((k) ^(i) ⁻¹⁾ may itself be a pre-SIC metric that does notconsider the interference cancellation of the codewords transmitted at aprevious transmission time. In other embodiments, this ordering metricγ_(i) ^((k) ^(i) ⁻¹⁾ may have considered cancellation interference ondecoding codeword i the (k_(i)−1)^(th) transmission attempt (i.e., γ_(i)^((k) ^(i) ⁻¹⁾ may be a post-SIC ordering metric).

In some embodiments, the pre-SIC ordering metric γ_(i,before) ^((k) ^(i)⁾ may be computed by combining the ordering metric γ_(i) ^((k) ^(i) ⁻¹⁾(pre-SIC or post-SIC) with pre-SIC SINR values. These pre-SIC SINRvalues (also referred to as SINR_(before)) may be computed assuming thecorresponding codeword i is decoded without any interferencecancellation. For example, these SINR_(before) values may be computed byassuming that the codewords are decoded using a linear equalizer with noSIC.

In some embodiments, the ordering metric γ_(i) ^((k) ^(i) ⁻¹⁾ may beadded to the codeword SINR value using a linear sum as follows:

$\begin{matrix}{{\gamma_{i,{before}}^{(k_{i})} = {\gamma_{i}^{({k_{i} - 1})} + {\frac{1}{{M\left( {t_{i}\left( k_{i} \right)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(k_{i})}})}}{{SINR}_{s,{before}}^{(k_{i})}(m)}}}}}},} & \left( {{EQ}.\mspace{14mu} 14} \right)\end{matrix}$where SINR_(s,before) ^((k) ^(i) ⁾(m) represents the streamSINR_(before) value for the s^(th) stream at the k_(i) ^(th)transmission attempt of codeword i. The second operand in EQ. 14 may bedefined as a codeword SINR value of codeword i at the k_(i) ^(th)transmission attempt. This codeword SINR value corresponds to theaverage of the stream SINR_(before) values (SINR_(s,before) ^((k) ^(i)⁾(m)) over all streams s and all coded symbols of codeword i at thek_(i) ^(th) transmission attempt. While EQ. 14 shows a linear sum, anyother combination function may be used to combine the recursive metricγ_(i) ^((k) ^(i) ⁻¹⁾ with the codeword SINR value, such as geometricsum.

At 854, a decoding ordering Π^((t)) may be determined based on thepre-SIC ordering metrics. For example, the decoding ordering may bedetermined by sorting the codewords based on their corresponding pre-SICordering metrics from highest to lowest. This may be represented asfollows:Π^((t))={(L ₁ ,L ₂ , . . . ,L _(C))|γ_(L) ₁ _(,before) ^((k) ^(i)_≧γ_(L) ₂ _(,before) ^((k) ^(i) ⁾≧ . . . ≧γ_(L) _(C) _(,before) ^((k)^(i) ⁾}.

At 856, the codewords may be decoded using SIC based on the determinedordering Π^((t)). For example, codewords L₁ through L_(C) may be decodedwith interference cancellation as described in FIG. 2 above.

At 858, an updated post-SIC ordering metric γ_(i) ^((k) ^(i) ⁾ may becomputed based on updated SINR values of codeword i that take intoaccount interference cancellation. These SINR values may correspond toSIC-adjusted channels and take into account the interferencecancellation gained from a codeword decoded in the ordering determinedat 854. For example, the ordering metric for codeword i associated withtransmission time t_(i)(k_(i)) may be updated using the followingrecursive equation:

$\begin{matrix}{{{\gamma_{i}^{(k_{i})} = {\gamma_{i}^{({k_{i} - 1})} + {\frac{1}{{M\left( {t_{i}\left( k_{i} \right)} \right)}{S_{i}}}{\sum\limits_{s \in S_{i}}{\sum\limits_{m = 1}^{M{({t_{i}{(k_{i})}})}}{{SINR}_{s,{after}}^{(k_{i})}(m)}}}}}};}{{\gamma_{i}^{(0)} = 0},}} & \left( {{EQ}.\mspace{14mu} 15} \right)\end{matrix}$wherein SINR_(s,after) ^((j)) represents the stream SINR_(after) valuefor the s^(th) stream at the j^(th) transmission attempt of codeword itaking into account the interference cancellation gain for codeword i.In one example, SINR_(after) may assume a SIC equalizer with perfectinterference cancellation (i.e., no error propagation between SICstages).

Although EQ. 15 above uses equalizer-output SINR values, this is meantto be illustrative and not limiting or exhaustive in any way. Any othersuitable performance metric may be used. For example, the SNR valuesused in the incremental SNR-based process 750 of FIG. 7B may beunderstood as a post-SIC SINR value since perfect interferencecancellation is assumed.

In some embodiments, if a codeword decoded at a specific SIC stage isnot recovered error-free, then errors may propagate to the interferencecancellation of subsequent SIC stages, thereby degrading performance.This is referred to as error propagation. In some embodiments, thepost-SIC SINR values may also account for error propagation andcompensate for it using error compensation (EC). This will beillustrated in FIG. 9 below.

FIG. 9 illustrates one example of the incremental SINR based orderingapproach of FIG. 8B, in accordance with some embodiments. FIG. 9 uses anexemplary MMSE equalizer in a 2×2 MIMO system with two codewords (i=1,2) and one stream per codeword (S_(i)={i}).

An example of pre-SIC SINR values, e.g., as used at 852 of FIG. 8Babove, is shown in EQ. 902 of FIG. 9. As can be seen from EQ. 902,SINR_(s,before)(m) values do not take into account interferencecancellation, and correspond to a linear MMSE equalizer SINR (i.e.,without SIC).

An example of post-SIC SINR values, e.g., as used at 858 of FIG. 8Babove, is shown in EQ. 904 of FIG. 9. This post-SIC SINR of EQ. 904takes into account the SIC ordering. Specifically, EQ. 904 considers theeffect of cancelling the interference due to the first decoded codewordL₁ from the second decoded codewords L₂. At 906, for the first decodedcodeword L₁, SINR_(s,after)(m) is the same as SINR_(s,before)(m), sinceno interference cancellation is applied to this first codeword. At 908,for the second decoded codeword L₂, SINR_(s,after)(m) takes into accountthe effect of cancelling the interference due to L₁ from L₂. Inparticular, as shown in EQ. 904, the SINR_(s,after)(m) for codeword L₂is based on the interference-adjusted channel h_(L) ₂ associated withcodewords L₂, e.g., obtained by removing the columns corresponding tothe channels for the first decoded codeword L₁ from the overalleffective channel H as described in FIG. 2 above.

As explained above, the post-SIC SINR values of EQ. 904 assume perfectinterference cancellation (i.e., these values do not take into accountany error propagation). In some embodiments, in addition to consideringthe effect of interference cancellation, the SINR_(s,after)(m) for thecodeword L₂ may also take into account error propagation. An example ofa post-SIC SINR values that consider both SIC ordering and errorcompensation is shown in EQ. 920. Like EQ. 904, EQ. 920 considers theeffect of SIC by using the interference-adjusted channel h_(L) ₂ .Additionally, EQ. 920 integrates an error compensation component 922 tocompensate for the error propagation from the first SIC decoding stage.

This error compensation component may correspond to an error between thereconstructed transmitted signal vector {circumflex over (x)}_(L) ₁ forcodeword L₁ (i.e., the feedback symbols as explained in FIG. 2 above)and the transmitted signal vector x_(L) ₁ (i.e., the actuallytransmitted symbols). This may be represented as an error varianceestimate corresponding to the first decoded codeword L₁ at the currenttransmission time (corresponding to transmission attempt k_(L) ₁ ) asfollows:

$\begin{matrix}{{E\left\lbrack {e}^{2} \right\rbrack} = {{E\left\lbrack {{x_{L_{1}}^{(k_{L_{1}})} - {\hat{x}}_{L_{1}}^{(k_{L_{1}})}}}^{2} \right\rbrack}.}} & \left( {{EQ}.\mspace{14mu} 16} \right)\end{matrix}$

In some embodiments, the error variance of EQ. 16 may be difficult orimpossible to compute. In this case, the error variance may beapproximated based on an estimated transmitted signal vector {tilde over(x)}_(L) _(i) , as follows:

${{E\left\lbrack {e}^{2} \right\rbrack} \approx {\frac{1}{M(t)}{\sum\limits_{m}{{{{\hat{x}}_{L_{1}}^{(k)}(m)} - {{\hat{x}}_{L_{1}}^{(k)}(m)}}}^{2}}}},$where the estimated transmitted signals {tilde over (x)}_(L) ₁ (m) areaveraged over M(t) coded symbols m transmitted at time t for codewordL₁. In some embodiments, the estimated transmitted signal vector {tildeover (x)}_(L) ₁ (m) may be determined based on soft information. Forexample, this soft information may be output by an equalizer based on alog-likelihood ratio (“LLR”) for each received symbol of intendedinformation.

FIGS. 10A and 10B (collectively referred to as FIG. 10 herein)illustrate the performance of three history-aware SIC ordering processes(incremental SNR, incremental SINR, and incremental SINR with errorcompensation) compared to a history-free SIC ordering process and adecoding process using a linear receiver (with no SIC). The simulationsare based on the PDSCH demodulation test case 5.2 specified in the 3GPPTS36.101 V8.8.0 “User Equipment (UE) radio transmission and reception”specification, which is hereby incorporated by reference in itsentirety. In the simulations of FIG. 10, a 2×2 MIMO low correlationimplementation is used with carrier bandwidth of 10 MHZ, 16QAMmodulation scheme, and code rate 1/2. The simulated systems transmit twocodewords (C=1) each mapped to one stream, and use a maximum of 4 HARQretransmissions and a random precoder with ideal channel estimation(CE). The simulated 5.2 test case is associated with a closed loop MIMO(CL-MIMO) system with spatial multiplexing (SM), random beamforming, andTU-70.

FIG. 10A shows a simulated performance of processes for determining SICordering in a closed loop MIMO system using minimum mean square error(MMSE) decoding, in accordance with embodiments of the presentdisclosure. The x axis represents Signal-to-Noise ratio (SNR) (indecibels (db)) and the y axis represents normalized throughput (i.e.,the percentage of the peak data rate).

The first graph labeled “MMSE,” corresponding to solid line 1,represents the performance of a decoding process that uses the linearreceiver without any interference cancellation.

The second graph labeled “MMSE-SIC (subframe SNR),” corresponding todashed line 2, represents the performance of the MMSE equalizer with SICusing a history-free SIC ordering. For this graph, the two codewords areordered based on the subframe channel gain (i.e., subframe SNR) at thereceiving time only, without regard to previous transmission attempts ofthe codewords. An MMSE equalizer is used to decode the first codeword L₁in the determined history-free SIC ordering. SIC is used to decode thesecond codeword L₁ in the determined ordering.

The third graph labeled “MMSE-SIC (sum SNR),” corresponding to line 3(marked with ‘o’), represents the performance of the incremental SNRordering using a linear sum of channel gains, e.g., as described in EQS.10 and 12 and FIGS. 7A and 7B above.

The fourth graph labeled “MMSE-SIC (sum SINR+EC),” corresponding to line4 (marked with ‘x’), represents the performance of the incremental SINRordering using a linear sum of MMSE-type SINR values (e.g., based on anMMSE criterion) and using error compensation, e.g., as described in EQS.13 and 16 and in FIGS. 8A, 8B, and 9B above. For this graph, anMMSE-type SINR_(before) is used to determine the SIC ordering of the twocodewords, and an MMSE-type SINR_(after) is used to update the orderingmetrics after performing SIC, as described in EQS. 14 and 15 and in FIG.8B above.

The fifth graph labeled “MMSE-SIC (sum SINR no EC),” corresponding toline 5 (marked with ‘*’), represents the performance of the incrementalSINR ordering using a linear sum of MMSE-type SINR values and no errorcompensation, e.g., as described in EQS. 13, 14, and 15, and in FIGS.8A, 8B, and 9A above. Similarly to the process of the fourth graph, anMMSE-type SINR_(before) is used to determine the SIC ordering of the twocodewords, and an MMSE-type SINR_(after) is used to update the orderingmetrics after performing SIC.

A comparison between the five performance graphs shows that theincremental SINR based approach with error compensation (i.e.,corresponding to graph 4) improves the performance gain at low SNRvalues and maintains the performance gain at high SNR values. Theincremental SINR based approach with EC is consistently better than thelinear receiver based approach (i.e., corresponding to graph 1). Acomparison between graphs 4 and 5 shows that error compensation may becritical for the incremental SINR approach in this particularsimulation. Also, the incremental SNR based approach (i.e.,corresponding to graph 3) improves the performance gain compared to thelinear receiver approach (i.e., corresponding to graph 1) and to theconventional MMSE-SIC approach (i.e., corresponding to graph 2), but theimprovement is slightly less than that of the incremental SINR basedapproach with EC (i.e., corresponding to graph 5).

FIG. 10B shows a simulated performance of processes for determining SICordering in a closed loop MIMO system using maximum likelihood decoding(MLD), in accordance with some embodiments of the present disclosure.The x axis represents Signal-to-Noise ratio (SNR) (in decibels (db)) andthe y axis represents normalized throughput. The five graphs correspondto the same processes illustrated in FIG. 10A, except that the equalizeruses MLD instead of MMSE.

A comparison between the five performance graphs shows that MLD-SICworks best with the incremental SNR based approach (i.e., correspondingto graph 3), which improves the performance gain at low SNR values andmaintains the performance gain at high SNR values. The incremental SINRbased approach (i.e., corresponding to graphs 4 and 5), which usesMMSE-type SINR values, does not appear to be optimal for the MLDperformance in this test case.

FIGS. 11A and 11B (collectively referred to as FIG. 11 herein)illustrate the performance of three history-aware SIC ordering processes(incremental SNR, incremental SINR, and incremental SINR with errorcompensation) compared to a history-free SIC ordering process and adecoding process using a linear receiver (with no SIC). The simulationsare based on the PDSCH demodulation test case 6.1 specified in the 3GPPTS36.101 V8.8.0 specification. A 2×2 MIMO low correlation implementationis used with carrier bandwidth of 10 MHZ, 16QAM modulation scheme, andcode rate 1/2. The simulated systems transmit two codewords (C=1) eachmapped to one stream, and use a maximum of 4 HARQ retransmissions and arandom precoder with ideal channel estimation (CE). The simulated 6.1test case is associated with an open loop MIMO (OL-MIMO) with largecyclic delay cyclic diversity (LD-CDD), and VA-70.

FIG. 11A shows a simulated performance of processes for determining SICordering in an open loop MIMO system using minimum mean square error(MMSE) decoding, in accordance with some embodiments of the presentdisclosure. The x axis represents Signal-to-Noise ratio (SNR) (indecibels (db)) and the y axis represents normalized throughput. The fivegraphs correspond to the same processes illustrated in FIG. 10A above.

A comparison of the performance graphs shows that, in this test case,SIC does not perform as well as a decoding process using a linearreceiver (with no SIC). This is because LD-CDD uses channels of the samequality for both transmitted codewords, so that SIC leads to errorpropagation but little interference cancellation gain. This is why thehistory-free SIC approach (i.e., corresponding to graph 2) does notperform well because it does not compensate for error propagation.Still, the incremental SNR based approach and the incremental SINR withEC based approach (i.e., corresponding to graphs 3 and 4) improve theperformance compared to the history-free SIC approach. In addition, theincremental SINR with EC based approach performs almost as well as thelinear receiver approach.

FIG. 11B shows a simulated performance of processes for determining SICorderings in an closed loop MIMO system using MLD, in accordance withsome embodiments of the present disclosure. The x axis representsSignal-to-Noise ratio (SNR) (in decibels (db)) and the y axis representsnormalized throughput. The five graphs correspond to the same processesillustrated in FIG. 10B above. In this test case, the incremental SNR(i.e., corresponding to graph 3) performs best compared to the SICprocesses, but still represents some loss compared to the linearreceiver approach because of the suboptimality of SIC in this particulartest case.

The above steps of the flowcharts of FIGS. 3, 4, 5, 6, 7A, 7B, 8A, and8B may generally be executed or performed in any order or sequence notlimited to the order and sequence shown and described in the figure.Also, some of the above steps of processes of FIGS. 3, 4, 5, 6, 7A, 7B,8A, and 8B may be executed or performed substantially simultaneouslywhere appropriate or in parallel to reduce latency and processing times.Any of the steps in these processes may be omitted, modified, combined,and/or rearranged, and any additional steps may be performed, withoutdeparting from the scope of the present disclosure.

The foregoing describes systems and methods for reliable and efficientinformation transmission. Those skilled in the art will appreciate thatthe disclosed methods and systems can be practiced by other than thedescribed embodiments, which are presented for the purpose ofillustration rather than of limitation. Modifications and variations arepossible in light of the above teachings or may be acquired frompractice of the disclosed methods and systems. For example, although thepresent disclosure primarily discusses using all transmission timesγ=t_(i)(1), . . . , t_(i)(k_(i)) for computing ordering metric γ_(i)(t)of a codeword i, starting from the first transmission attempt throughthe last transmission attempt at time t, any appropriate subset of τ maybe used in this computation. For example, only a last number oftransmission attempts may be used. While certain components of thisdisclosure have been described as implemented in hardware and others insoftware, other configurations may be possible.

What is claimed is:
 1. A method for determining a successiveinterference cancellation (SIC) ordering in a system with aretransmission protocol, the method comprising: receiving a plurality ofcodewords that are transmitted in a current transmission time, whereinat least one of the plurality of codewords was previously transmitted ina previous transmission time; for the at least one previouslytransmitted codeword, computing an ordering metric for the codewordbased on i) a first channel associated with the previous transmissiontime and ii) a second channel associated with the current transmissiontime; and determining a decoding ordering of the codewords based on thecomputed ordering metric.
 2. The method of claim 1, wherein computingthe ordering metric for the at least one previously transmitted codewordcomprises computing the ordering metric based on channels associatedwith any subset of all transmission times corresponding to alltransmission attempts of the codeword.
 3. The method of claim 1, whereincomputing the ordering metric for the at least one previouslytransmitted codeword comprises: mapping the first and second channels toan effective Signal-to-Noise ratio (SNR) value for each uniquetransmitted symbol of the codeword; and estimating a Packet Error Rate(PER) value of the codeword based on the effective SNR values.
 4. Themethod of claim 1, wherein computing the ordering metric for the atleast one previously transmitted codeword comprises combining i) a firstchannel gain associated with the previous transmission time and ii) asecond channel gain associated with the current transmission time. 5.The method of claim 1, wherein computing the ordering metric for the atleast one previously transmitted codeword comprises combining i) a firstequalizer-output Signal-to-Interference and Noise Ratio (SINR) valueassociated with the previous transmission time and ii) a secondequalizer-output SINR value associated with the current transmissiontime.
 6. The method of claim 1, wherein computing the ordering metricfor the at least one previously transmitted codeword comprises:initializing a recursive metric for the codeword prior to a firsttransmission attempt of the codeword; and updating the recursive metricfor a k^(th) transmission attempt of the codeword based on a value ofthe recursive metric for a (k−1)^(th) transmission attempt of thecodeword.
 7. The method of claim 6, further comprising: determining thatthe codeword was successfully transmitted at the current transmissiontime; and resetting the recursive metric in response to determining thatthe codeword was successfully transmitted.
 8. The method of claim 6,further comprising: computing an ordering metric for the k^(th)transmission attempt of the codeword based on i) the value of therecursive metric for a (k−1)^(th) transmission attempt of the codewordand ii) a performance metric, wherein the performance metric isdetermined prior to performing interference cancellation; determiningthe decoding order based on the initial recursive metric; computing anupdated performance metric based on the determined decoding order; andupdating the recursive metric at the k^(th) transmission attempt of thecodeword based on i) the value of the recursive metric for a (k−1)^(th)transmission attempt of the codeword and ii) the updated performancemetric.
 9. The method of claim 1, further comprising: estimating anerror due to decoding a first codeword; and estimating a performancemetric for a second codeword based on the estimated error, wherein thesecond codeword is decoded after the first codeword, and wherein aninterference from the first codeword is cancelled from the secondcodeword.
 10. The method of claim 1, wherein the retransmission protocolis selected from the group consisting of a hybrid automatic repeatrequest (HARQ) protocol, an automatic repeat request (ARQ) protocol, anda repetition coding and transmission protocol.
 11. A receiver fordetermining a successive interference cancellation (SIC) ordering for aplurality of codewords, the receiver comprising processing circuitryconfigured to: receive a plurality of codewords that are transmitted ina current transmission time, wherein at least one of the plurality ofcodewords was previously transmitted in a previous transmission time;for the at least one previously transmitted codeword, compute anordering metric for the codeword based on i) a first channel associatedwith the previous transmission time and ii) a second channel associatedwith the current transmission time; and determine a decoding ordering ofthe codewords based on the computed ordering metric.
 12. The receiver ofclaim 11, wherein the processing circuitry is further configured tocompute the ordering metric based on channels associated with any subsetof all transmission times corresponding to all transmission attempts ofthe codeword.
 13. The receiver of claim 11, wherein the processingcircuitry is further configured to: map the first and second channels toan effective Signal-to-Noise ratio (SNR) value for each uniquetransmitted symbol of the codeword; and estimate a Packet Error Rate(PER) value of the codeword based on the effective SNR values.
 14. Thereceiver of claim 11, wherein the processing circuitry is furtherconfigured to combine i) a first channel gain associated with theprevious transmission time and ii) a second channel gain associated withthe current transmission time.
 15. The receiver of claim 11, wherein theprocessing circuitry is further configured to combine i) a firstequalizer-output Signal-to-Interference and Noise Ratio (SINR) valueassociated with the previous transmission time and ii) a secondequalizer-output SINR value associated with the current transmissiontime.
 16. The receiver of claim 11, wherein the processing circuitry isfurther configured to: initialize a recursive metric for the codewordprior to a first transmission attempt of the codeword; and update therecursive metric for a k^(th) transmission attempt of the codeword basedon a value of the recursive metric for a (k−1)^(th) transmission attemptof the codeword.
 17. The receiver of claim 16, wherein the processingcircuitry is further configured to: determine that the codeword wassuccessfully transmitted at the current transmission time; and reset therecursive metric in response to determining that the codeword wassuccessfully transmitted.
 18. The receiver of claim 16, wherein theprocessing circuitry is further configured to: compute an orderingmetric for the k^(th) transmission attempt of the codeword based on i)the value of the recursive metric for a (k−1)^(th) transmission attemptof the codeword and ii) a performance metric, wherein the performancemetric is determined prior to performing interference cancellation;determine the decoding order based on the initial recursive metric;compute an updated performance metric based on the determined decodingorder; and update the recursive metric at the k^(th) transmissionattempt of the codeword based on i) the value of the recursive metricfor a (k−1)^(th) transmission attempt of the codeword and ii) theupdated performance metric.
 19. The receiver of claim 11, wherein theprocessing circuitry is further configured to: estimate an error due todecoding a first codeword; and estimate a performance metric for asecond codeword based on the estimated error, wherein the secondcodeword is decoded after the first codeword, and wherein aninterference from the first codeword is cancelled from the secondcodeword.
 20. The receiver of claim 11, wherein the wherein theretransmission protocol is selected from the group consisting of ahybrid automatic repeat request (HARQ) protocol, an automatic repeatrequest (ARQ) protocol, and a repetition coding and transmissionprotocol.